Abstract

The ISO 19906 local pressure-area relationship represents a deterministic estimate of the failure pressure of massive ice features. For areas < 10 m2 the pressure is represented as a power law on area. For areas between 10 and 40 m2 the pressure has a constant value. In the past, in order to fit the power law, the data were binned and means and standard deviations for each bin were determined. The deterministic value of the local ice failure pressure is the relationship obtained by fitting a line to the values of mean plus three standard deviations so obtained. This implies the probability a local ice pressure exceeds the deterministic relationship is 0.13%, treating the deterministic value as a one-sided upper bound. It is shown herein that a quantitative, repeatable and non-subjective statistical methodology called quantile regression can be applied to this data. Using a nonlinear quantile regression methodology the deterministic relationship can be estimated in one step without the requirement for binning or transformation. Furthermore, the method produces quantile lines for a wide range of quantiles. The nonlinear quantile regression analysis of the local pressure area relationship, fitted to a power law, indicate the deterministic ISO relationship is in fact equivalent to an exceedance of 5% for areas greater than 2 and less than 10 m2. For areas of less than 2 m2 the ISO relationship exceedance decreases from 5% at 2 m2 to less than 1% for areas less than 0.3 m2.

The purpose of this paper is to introduce this powerful technique to the ice science and ice engineering communities using the local ice pressure data as an example.

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